Existence Of Critical State Research Articles

Milu-CG method and the numerical study on the flow around a rotating circular cylinder

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number Re=1000, 200 and the angular to rectilinear speed ratio a∈(0.5,3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

Buckling Mode Interaction in Composite Plate Assemblies

The analysis of buckling mode interaction of fiber-reinforced composite columns, modeled as plate assemblies, is presented. The main assumptions are linear elasticity; a linear fundamental equilibrium path; the existence of critical states that are coincident or near coincident; and a coupled path rising from a quadratic combination of modal displacements due to interaction. The formulation adopted is known as the W-formulation, in which the energy is written in terms of a sliding set of incremental coordinates, measured with respect to the fundamental path. The energy is then expressed with respect to a reduced modal coordinate basis, and the coupled solution arising from interaction is computed. An example of a pultruded composite I-column subjected to axial compression illustrates the procedure.

Theory of nucleation in finite systems—Illustrated by ethanol condensation

A complete thermodynamic and kinetic model for nucleation and condensation in an isothermalisocoric finite system is presented, which allows exact calculation of all characteristic data of the condensation process. The main difference between classical isobaric nucleation theory and the condensation theory in finite systems is the existence of critical states, maxima of the Helmholtz free energy of condensation, besides metastable states, minima of the Helmholtz free energy of condensation in a finite system whereas only a critical state is found under isobaric conditions. Dependent on the initial supersaturation a first critical and a first metastable droplet size exist in a finite system, and a complete condensation curve is obtained for one single supersaturation. This curve describes the path from supersaturated vapor to the stable equilibrium of bulk liquid at saturation vapor pressure. Different definitions of nucleation rate, condensation rate, and droplet growth rate are compared with each other. Relations between these quantities are derived. Comparison of the present theory to experimental results of ethanol condensation shows good quantitative agreement.